Topological Methods in Nonlinear Analysis

Existence of solutions for a nonlinear wave equation

Marek Galewski and Andrzej Nowakowski

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Abstract

We prove the existence of a strong solution of a periodic-Dirichlet problem for the semilinear wave equation with irrational period and with nonlinearity satisfying some general growth conditions locally around $0$. We construct a new variational method, called a dual method, and using relations between critical points and critical values of the primal action and the dual action functionals we prove that the solution exists. The dual functional which we define is different from the ones known so far in that it depends on two dual variables.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 28, Number 2 (2006), 385-399.

Dates
First available in Project Euclid: 13 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1463144822

Mathematical Reviews number (MathSciNet)
MR2289692

Zentralblatt MATH identifier
1134.35078

Citation

Galewski, Marek; Nowakowski, Andrzej. Existence of solutions for a nonlinear wave equation. Topol. Methods Nonlinear Anal. 28 (2006), no. 2, 385--399. https://projecteuclid.org/euclid.tmna/1463144822


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